Add TI-DeepONet DPC heat notebook example

[Parv621]

Notebook: Add TI-DeepONet DPC heat notebook example

Summary

• Add a differentiable predictive control (DPC) notebook for the heat equation using a trained TI-DeepONet model within Neuromancer. Demonstrates end-to-end policy learning via long-horizon rollouts with differentiable physics.

Changes

• examples/control/Part_7_TIDON_DPC_HEAT.ipynb adds a DPC example for PDE control based on TI-DeepONet, including problem setup, policy parameterization, rollout-based loss construction, and training using Neuromancer.

Context

• Recreates the DPC framework for PDE control using TI-DeepONet (time-integrated Deep Operator Network), following the methodology in prior DPC literature and the reference implementation in PDEControl_DPC.
• Uses a pretrained TI-DeepONet model from examples/neural_operators/Part_8_TIDON_HEAT.ipynb as a differentiable surrogate of the heat-equation dynamics.
• The neural operator enables backpropagation through long rollouts, allowing gradients of the control objective with respect to policy parameters.
• The objective is to learn a feedback control policy for a distributed parameter system using differentiable predictive control implemented in Neuromancer.

References

• Sarkar, D. R., Drgoňa, J., & Goswami, S. (2025). Learning to Control PDEs with Differentiable Predictive Control and Time-Integrated Neural Operators. arXiv:2511.08992.

Testing

• Not run (not needed).

[drgona]

@Parv621 both the file and notebook have import that is not included in the toml file

import gpytorch

Do we need this?

[Parv621]

@Parv621 both the file and notebook have import that is not included in the toml file

import gpytorch

Do we need this?

Added dependency as discussed

[drgona]

@Parv621 the examples also contain custom file paths:
data_path = "/home/pk222/projects/PDEControl_DPC/datasets/heat_smooth_f_dataset.npz"

Please remove all unnecessary data loads, the notebooks should be self-contained.
If really necessary to load any sort of file, do it in a similar fashin we handle it in this notebook:
neural DAEs

code example:

# Raw URL of area.dat
url = "https://raw.githubusercontent.com/pnnl/NeuralDAEs/master/training/area.dat"

# Download and save the file locally
response = requests.get(url)
with open("area.dat", "wb") as f:
    f.write(response.content)
area_data = np.loadtxt('area.dat')

[Parv621]

@Parv621 the examples also contain custom file paths: data_path = "/home/pk222/projects/PDEControl_DPC/datasets/heat_smooth_f_dataset.npz"

Please remove all unnecessary data loads, the notebooks should be self-contained. If really necessary to load any sort of file, do it in a similar fashin we handle it in this notebook: neural DAEs

code example:

# Raw URL of area.dat
url = "https://raw.githubusercontent.com/pnnl/NeuralDAEs/master/training/area.dat"

# Download and save the file locally
response = requests.get(url)
with open("area.dat", "wb") as f:
    f.write(response.content)
area_data = np.loadtxt('area.dat')

Added open OneDrive links for the best model